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Foundations of Celestial Mechanics

Elena Bannikova,Massimo Capaccioli

Author : Elena Bannikova,Massimo Capaccioli
Publisher : Springer
Page : 0 pages
File Size : 52,5 Mb
Release : 2022-09-13
Category : Science
ISBN : 3031045750

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Foundations of Celestial Mechanics by Elena Bannikova,Massimo Capaccioli Pdf

This book provides an introduction to classical celestial mechanics. It is based on lectures delivered by the authors over many years at both Padua University (MC) and V.N. Karazin Kharkiv National University (EB). The book aims to provide a mathematical description of the gravitational interaction of celestial bodies. The approach to the problem is purely formal. It allows the authors to write equations of motion and solve them to the greatest degree possible, either exactly or by approximate techniques, when there is no other way. The results obtained provide predictions that can be compared with the observations. Five chapters are supplemented by appendices that review certain mathematical tools, deepen some questions (so as not to interrupt the logic of the mainframe with heavy technicalities), give some examples, and provide an overview of special functions useful here, as well as in many other fields of physics. The authors also present the original investigation of torus potential. This book is aimed at senior undergraduate students of physics or astrophysics, as well as graduate students undertaking a master’s degree or Ph.D.

The Foundations of Celestial Mechanics

George William Collins

Author : George William Collins
Publisher : Unknown
Page : 166 pages
File Size : 50,7 Mb
Release : 1989
Category : Science
ISBN : UCAL:B4399149

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The Foundations of Celestial Mechanics by George William Collins Pdf

The Analytical Foundations of Celestial Mechanics

Aurel Wintner

Author : Aurel Wintner
Publisher : Unknown
Page : 468 pages
File Size : 54,9 Mb
Release : 1941
Category : Science
ISBN : UCAL:$B35463

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The Analytical Foundations of Celestial Mechanics by Aurel Wintner Pdf

The Analytical Foundations of Celestial Mechanics

Aurel Frederick Wintner

Author : Aurel Frederick Wintner
Publisher : Unknown
Page : 0 pages
File Size : 55,6 Mb
Release : 1941
Category : Celestial mechanics
ISBN : LCCN:nun00509730

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The Analytical Foundations of Celestial Mechanics by Aurel Frederick Wintner Pdf

New Foundations for Classical Mechanics

D. Hestenes

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400948020

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New Foundations for Classical Mechanics by D. Hestenes Pdf

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

New Foundations for Classical Mechanics

D. Hestenes

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 40,9 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471223

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New Foundations for Classical Mechanics by D. Hestenes Pdf

(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Foundations Of Mechanics

Ralph Abraham

Author : Ralph Abraham
Publisher : CRC Press
Page : 850 pages
File Size : 55,8 Mb
Release : 2019-04-24
Category : Science
ISBN : 9780429709050

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Foundations Of Mechanics by Ralph Abraham Pdf

Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

Mathematical Aspects of Classical and Celestial Mechanics

Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt

Author : Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 49,5 Mb
Release : 2007-07-05
Category : Mathematics
ISBN : 9783540489269

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Mathematical Aspects of Classical and Celestial Mechanics by Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt Pdf

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Essential Relativistic Celestial Mechanics

Victor Brumberg

Author : Victor Brumberg
Publisher : CRC Press
Page : 274 pages
File Size : 45,5 Mb
Release : 2017-11-22
Category : Science
ISBN : 9781351449694

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Essential Relativistic Celestial Mechanics by Victor Brumberg Pdf

Essential Relativistic Celestial Mechanics presents a systematic exposition of the essential questions of relativistic celestial mechanics and their relation to relativistic astrometry. The book focuses on the comparison of calculated and measurable quantities that is of paramount importance in using general relativity as a necessary framework in the discussion of high-precision observations and for the construction of accurate dynamical ephemerides. It discusses the results of the general relativistic theory of motion of celestial bodies and describes the relativistic theory of astronomical reference frames, time scales, and the reduction of observations.

Meanest Foundations and Nobler Superstructures

Ofer Gal

Author : Ofer Gal
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 55,9 Mb
Release : 2013-11-11
Category : History
ISBN : 9789401722230

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Meanest Foundations and Nobler Superstructures by Ofer Gal Pdf

This book is a historical-epistemological study of one of the most consequential breakthroughs in the history of celestial mechanics: Robert Hooke's (1635-1703) proposal to "compoun[d] the celestial motions of the planets of a direct motion by the tangent & an attractive motion towards a centrat body" (Newton, The Correspondence li, 297. Henceforth: Correspondence). This is the challenge Hooke presented to Isaac Newton (1642-1727) in a short but intense correspondence in the winter of 1679-80, which set Newton on course for his 1687 Principia, transforming the very concept of "the planetary heavens" in the process (Herivel, 301: De Motu, Version III). 1 It is difficult to overstate the novelty of Hooke 's Programme • The celestial motions, it suggested, those proverbial symbols of stability and immutability, werein fact a process of continuous change: a deflection of the planets from original rectilinear paths by "a centraU attractive power" (Correspondence, li, 313). There was nothing necessary or essential in the shape of planetary orbits. Already known to be "not circular nor concentricall" (ibid. ), Hooke claimed that these apparently closed "curve Line[ s ]" should be understood and calculated as mere effects of rectilinear motions and rectilinear attraction. And as Newton was quick to realize, this also implied that "the planets neither move exactly in ellipse nor revolve twice in the same orbit, so that there are as many orbits to a planet as it has revolutions" (Herivel, 301: De Motu, Version III).

Relativistic Celestial Mechanics of the Solar System

Sergei Kopeikin,Michael Efroimsky,George Kaplan

Author : Sergei Kopeikin,Michael Efroimsky,George Kaplan
Publisher : John Wiley & Sons
Page : 897 pages
File Size : 42,7 Mb
Release : 2011-10-25
Category : Science
ISBN : 9783527634576

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Relativistic Celestial Mechanics of the Solar System by Sergei Kopeikin,Michael Efroimsky,George Kaplan Pdf

This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping.

Second Year Calculus

David M. Bressoud

Author : David M. Bressoud
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209591

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Second Year Calculus by David M. Bressoud Pdf

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

Leonhard Euler and the Foundations of Celestial Mechanics

Dora Musielak

Author : Dora Musielak
Publisher : Springer Nature
Page : 228 pages
File Size : 41,7 Mb
Release : 2022-11-01
Category : Science
ISBN : 9783031123221

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Leonhard Euler and the Foundations of Celestial Mechanics by Dora Musielak Pdf

The intention of this book is to shine a bright light on the intellectual context of Euler’s contributions to physics and mathematical astronomy. Leonhard Euler is one of the most important figures in the history of science, a blind genius who introduced mathematical concepts and many analytical tools to help us understand and describe the universe. Euler also made a monumental contribution to astronomy and orbital mechanics, developing what he called astronomia mechanica. Orbital mechanics of artificial satellites and spacecraft is based on Euler’s analysis of astromechanics. However, previous books have often neglected many of his discoveries in this field. For example, orbital mechanics texts refer to the five equilibrium points in the Sun-Earth-Moon system as Lagrange points, failing to credit Euler who first derived the differential equations for the general n-body problem and who discovered the three collinear points in the three-body problem of celestial mechanics. These equilibrium points are essential today in space exploration; the James Webb Space Telescope (successor to the Hubble), for example, now orbits the Sun near L2, one of the collinear points of the Sun-Earth-Moon system, while future missions to study the universe will place observatories in orbit around Sun-Earth and Earth-Moon equilibrium points that should be properly called Euler-Lagrange points. In this book, the author uses Euler’s memoirs, correspondence, and other scholarly sources to explore how he established the mathematical groundwork for the rigorous study of motion in our Solar System. The reader will learn how he studied comets and eclipses, derived planetary orbits, and pioneered the study of planetary perturbations, and how, old and blind, Euler put forward the most advanced lunar theory of his time.